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Rates of decay for the survival probability of a mutant gene

โœ Scribed by K. B. Athreya

Publisher
Springer
Year
1992
Tongue
English
Weight
203 KB
Volume
30
Category
Article
ISSN
0303-6812

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โœฆ Synopsis

If q~ is the extinction probability of a slightly supercritical branching process with offspring distribution (Pgr "r = 0, 1, 2 . . . . }, then it is shown that if

2 This provides a simple set of sufficient condi-

tions for the validity of a conjecture of Ewens (1969) for the survival probability of a slightly advantageous mutant gene.

๐Ÿ“œ SIMILAR VOLUMES

Asymptotic rates of growth of the extinc
Asymptotic rates of growth of the extinction probability of a mutant gene
โœ Fred M. Hoppe ๐Ÿ“‚ Article ๐Ÿ“… 1992 ๐Ÿ› Springer ๐ŸŒ English โš– 876 KB

We prove that a result of Haldane (1927) that relates the asymptotic behaviour of the extinction probability of a slightly supercritical Poisson branching process to the mean number of offspring is true for a general Bienaym6-G a l t o n -W a t s o n branching process, provided that the second deriv

The survival probability of a mutant in
The survival probability of a mutant in a multidimensional population
โœ Fred M. Hoppe ๐Ÿ“‚ Article ๐Ÿ“… 1992 ๐Ÿ› Springer ๐ŸŒ English โš– 379 KB

We prove a general result about the asymptotic behaviour of the survival probability of a slightly supercritical multitype Bienaym6-Galton-Watson branching process. This is the complete analogue of a result which Ewens (1968) obtained for a Poisson branching process.